"We know we are capable of putting together wins if we play like this," Vanek said. "We have to get better, but when we stay patient, we can win against anyone."

Montreal (27-12-6) is 2-3-0 in its past five games. Carey Price made 19 saves.

"I wish we could have generated more offensive chances, but they did a very good job of stopping us in the neutral zone," Canadiens coach Michel Therrien said. "We played well defensively, and Carey was very good, but we didn't get any puck luck."

Price was happy with his performance after allowing 18 goals in the past four games.

"I was just keeping things simple and letting the puck come to me," he said. "I got lucky on a couple tips, but it was better."

Detroit nearly took a 1-0 lead on a power play in the second period, but Vanek's tip bounced just past the post, and Price stopped his next chance moments later.

Vanek broke the scoreless tie at 18:14 of the second, scoring his fifth goal in six games. Danny DeKeyser's shot from the point deflected off Vanek's hip and past Price for his team-high 12th goal.

"He's got an unbelievable offensive mind," Red Wings coach Jeff Blashill said of Vanek. "He had the tip that got behind Price and probably should have gone in, and then he gets the goal. He's been a really good fit for us."

Shea Weber had Montreal's best chance of the third period but Coreau made a juggling catch of his shot from the point.

"I'm just trying to be calm and stay sound technically," said Coreau, who shut out the Los Angeles Kings in a 4-0 win on Jan. 5. "I'm going to enjoy this, but I can't get too high, because a shutout is definitely a team effort."

The Canadiens had trouble pulling Price at the end, needing nearly 40 seconds before getting a sixth skater on to the ice.

"They really shut us down in the neutral zone," Canadiens forward Paul Byron said. "We tried to use our speed, but they did a great job of taking that away from us."

Goal of the game

On the game's only goal, Nielsen collected a rebound in front of the net and got the puck back to DeKeyser at the point. His slap shot was heading to the right of the net, but ricocheted off Vanek when he struggled to get free of Alexei Emelin.

Highlight of the game

With the game still scoreless in the second period, Montreal had a 2-on-1 break. Max Pacioretty fooled the Detroit defense with a drop pass to Alex Galchenyuk, but Coreau dropped into the butterfly to stop his shot from between the hash marks.

"I know that, with my size, if I stay back in the crease, a lot of pucks are going to hit me," said Coreau, who is 6-foot-6, 220 pounds. "I work on that a lot, just making sure to keep the puck in front of me."

Unsung moment of the game

In the first period, with Montreal pressing, Red Wings forward Luke Glendening broke his stick, giving the Canadiens a chance to score. Glendening, though, drew a big cheer from the crowd by throwing himself in front of Weber's slap shot, allowing Detroit to clear the zone.

They said it

"I thought we played very well, but it wasn't perfect. No one ever plays a perfect game in this league." -- Canadiens captain Max Pacioretty

"It probably wasn't the most fun game to watch, with two teams that played really tight and two goalies that played well, but we're happy with it." -- Red Wings captain Henrik Zetterberg

Need to know

Montreal forward Jacob De La Rose made his season debut, one day after being recalled from St. John's of the American Hockey League. … Glendening and Drew Miller, playing together on Detroit's checking line, each blocked three shots.